Existence of a positive solution to a nonlinear system of PDEs in a domain with a triple-phase boundary

Abstract

We consider a system of nonlinear PDEs describing the reaction-diffusion dynamics near a triple-phase boundary in the catalyst layer of hydrogen fuel cells. The system involves bulk diffusion and surface reaction-diffusion processes and is an approximation of a model with a thin layer. The coupling of surface and bulk diffusion involves a nonlinear equation (adsorption-desorption process) and a singular boundary condition. Using certain a priori estimates, variational methods techniques and the fixed point theorem, we prove the existence of a positive bounded weak solution. Moreover, we prove the validity of the model by computing the solution numerically and comparing it with the solution obtained with a thin layer model.